~Chapter 10: Quadratic Equations and Functions~Shauna's Wiki! :)Here's a link to an online graphing calculator: http://www.coolmath.com/graphit/
10-1: Exploring Quadratic Graphs
A quadratic function is a function that can be written in the form y = ax2 + bx + c.
This form is called the standard form of a quadratic function.
The simplest quadratic function, f(x) = x2 or y = x2, is the quadratic parent function.
The graph of a quadratic function is a U-shaped curve called a parabola.
The fold or line that divides the parabola into two matching halves is called the axis of symmetry.
The highest or lowest point of a parabola is its vertex, which is on the axis of symmetry.
The vertex is the minimum point or lowest point of the parabola.
The vertex is the maximum point or highest point of the parabola.
10-2: Quadratic Functions
Example: y = 2x2 + 4x - 3
Step 1 - What is the axis of symmetry?
x = -b / 2a b = 4 a = 2
x = -4 / 2(2) = -1
Step 2 - What is the vertex?
y = 2(-1+ 4(-1) -3)2
y = - 2 - 4 – 3 y = -5 Step 3 - What is the y-intercept? y = 2(0)2 + 4(0) – 3 y = -3 Step 4 - One more! y = 2(1)2 + 4(1) – 3 y = 2 + 4 – 3 y = 3
10-3: Solving Quadratic Equations
A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0. This form is called the standard form of a quadratic equation.
A quadratic equation can have two, one, or no real-number solutions. The solutions of a quadratic equation and the related x-intercepts are often called roots of the equation or zeros of the function.
10-1: Exploring Quadratic Graphs
A quadratic function is a function that can be written in the form y = ax2 + bx + c.
This form is called the standard form of a quadratic function.
The simplest quadratic function, f(x) = x2 or y = x2, is the quadratic parent function.
The graph of a quadratic function is a U-shaped curve called a parabola.
The fold or line that divides the parabola into two matching halves is called the axis of symmetry.
The highest or lowest point of a parabola is its vertex, which is on the axis of symmetry.
The vertex is the minimum point or lowest point of the parabola.
The vertex is the maximum point or highest point of the parabola.
10-2: Quadratic Functions
Example: y = 2x2 + 4x - 3
Step 1 - What is the axis of symmetry?
x = -b / 2ab = 4 a = 2
x = -4 / 2(2) = -1
Step 2 - What is the vertex?
y = 2(-1+ 4(-1) -3)2
y = - 2 - 4 – 3y = -5
Step 3 - What is the y-intercept?
y = 2(0)2 + 4(0) – 3
y = -3
Step 4 - One more!
y = 2(1)2 + 4(1) – 3
y = 2 + 4 – 3
y = 3
10-3: Solving Quadratic Equations
A quadratic equation is an equation that can be written in the form ax2 + bx + c = 0. This form is called the standard form of a quadratic equation.
A quadratic equation can have two, one, or no real-number solutions. The solutions of a quadratic equation and the related x-intercepts are often called roots of the equation or zeros of the function.